A k-bit integer n satisfying 0≦n≦2k−1 has a modular factorization n=|(−1)s2p3e|2k. Integer n may be represented by an exponent representation such as the exponent triple (s,p,e), where 0≦s≦1, 0≦p≦k, and 0≦e≦2k−2−1. A discrete logarithmic system (DLS) may represent integers n by their corresponding exponent triples (s,p,e). By doing this, integer multiplication may be reduced to addition of corresponding terms of the triples.
Known techniques for determining the exponent triple for a k-bit integer involve tables that grow exponentially with respect to k. These tables, however, are of limited use for representation of k-bit integers for k≧16. Accordingly, these known techniques are not efficient in certain situations.